= Solution
Take the M–C–O direction as $z$. <carbon monoxide> binds through <carbon> because its occupied $5\sigma$ donor orbital has a substantial carbon-end lobe. End-on overlap with an empty <metal> orbital of sigma symmetry gives \b[CO-to-metal <sigma donation>]. At the same time, occupied <metal> $d_{xz}$ and $d_{yz}$ orbitals overlap sideways with the two corresponding empty CO $2\pi^*$ orbitals, giving \b[metal-to-CO <pi backbonding>]. Both channels strengthen the <metal>–<carbon> bond, while backbonding lowers the internal C–O <bond order>. The processes are synergic: <sigma donation> helps supply <metal> <electron> density for backbonding, while backbonding relieves <electron> accumulation at the <metal>.
\Image[/past-exam-of-the-chemistry-b-course-of-the-university-of-cambridge/2021/paper-2-carbonyl-orbitals.png]
{title=Complementary sigma donation and pi backbonding in a metal carbonyl}
The original orbital sketch shows one of the two perpendicular pi channels. It is the occupied <metal> orbital, rather than an empty <metal> orbital, that supplies <electrons> to CO <antibonding orbitals>.
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